How it works
The pulley ratio is the driven pulley diameter divided by the driver pulley diameter:
i = D₂ / D₁
A ratio above 1:1 is a reduction — the driven pulley turns slower
than the driver. The driven speed is inversely proportional to diameter:
n₂ = n₁ · D₁ / D₂.
The belt (surface) speed is how fast the belt travels along the rim:
v = π · D · n. Because the belt does not slip, it runs at the same
surface speed on both pulleys, so either one gives the same result — here we use the
driver. Use the pitch (effective) diameter, not the outer rim.
Worked example
A 100 mm driver pulley driving a 250 mm driven pulley is a 2.5:1
reduction. At 1,750 RPM in, the driven pulley turns
1750 × 100 / 250 = 700 RPM. The belt surface speed is
π × 0.1 m × (1750 / 60) ≈ 9.16 m/s. Those are the numbers the
calculator shows for these inputs.
Frequently asked questions
- How do I calculate pulley ratio and RPM?
- The pulley ratio is the driven diameter divided by the driver diameter: ratio = D₂ / D₁. The driven speed is n₂ = n₁ · D₁ / D₂. For example a 100 mm driver and a 250 mm driven pulley is a 2.5:1 ratio, so a 1,750 RPM motor turns the driven pulley at 700 RPM.
- How does pulley size change speed?
- A bigger driven pulley turns slower. Speed is inversely proportional to diameter: if the driven pulley is twice the diameter of the driver, it turns at half the speed (and vice versa). Increasing the driver diameter speeds the driven pulley up.
- What is belt speed (surface speed)?
- Belt speed is how fast the belt travels along the pulley rim: v = π · D · n, using the driver diameter D and its speed n. Because the belt does not slip, it runs at the same surface speed on both pulleys. It is reported here in m/s (or ft/min in imperial).
- How do I find the driver size for a target driven RPM?
- Rearrange n₂ = n₁ · D₁ / D₂ to D₁ = D₂ · n₂ / n₁. Pick the driven pulley diameter and speed you need, then size the driver. Or, holding the driver fixed, the driven diameter is D₂ = D₁ · n₁ / n₂.
- Should I use the outer diameter or the pitch diameter?
- Use the pitch (effective) diameter, not the outer rim. For a V-belt the belt rides below the top of the groove, so the pitch diameter is slightly smaller than the OD; using the OD overstates the ratio.
- Does this work in metric and imperial?
- Yes — enter the pulley diameters in mm or inches, and belt speed is shown in m/s or ft/min. Toggle SI/Imperial in the header.
Method & assumptions
- No belt slip — the belt runs at the same surface speed on both pulleys, so the speed ratio equals the diameter ratio.
- Diameters are pitch (effective) diameters, not the outer rim; for a V-belt the pitch diameter is slightly smaller than the OD.
- Ignores belt creep and the small slip of real friction (flat / V) belts; toothed (timing) belts have effectively zero slip.
Related calculators
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- Belt Length Calculator — Two-pulley belt length and wrap angle from center distance and diameters.
- Chain Length Calculator — Roller-chain length in links and mm from sprocket teeth and center distance.
- Bearing Life (L10) Calculator — Basic L10 rating life in revolutions and hours from load, speed and rating.